Theorem peano2no

Description: A theorem for surreals that is analagous to the second Peano postulate peano2 . (Contributed by Scott Fenton, 17-Mar-2025)

	Ref	Expression
Assertion	peano2no	⊢ ( 𝐴 ∈ No → ( 𝐴 +s 1s ) ∈ No )

Proof

Step	Hyp	Ref	Expression
1		1sno	⊢ 1s ∈ No
2		addscl	⊢ ( ( 𝐴 ∈ No ∧ 1s ∈ No ) → ( 𝐴 +s 1s ) ∈ No )
3	1 2	mpan2	⊢ ( 𝐴 ∈ No → ( 𝐴 +s 1s ) ∈ No )